For the following exercises, find the values for each function, if they exist, then simplify. a. f ( 0 ) b. f ( 1 ) c. f ( 3 ) d. f ( − x ) e. f ( a ) f . f ( a + h ) 12. f ( x ) = x − 2 3 x + 7
For the following exercises, find the values for each function, if they exist, then simplify. a. f ( 0 ) b. f ( 1 ) c. f ( 3 ) d. f ( − x ) e. f ( a ) f . f ( a + h ) 12. f ( x ) = x − 2 3 x + 7
Points z1 and z2 are shown on the graph.z1 is at (4 real,6 imaginary), z2 is at (-5 real, 2 imaginary)Part A: Identify the points in standard form and find the distance between them.Part B: Give the complex conjugate of z2 and explain how to find it geometrically.Part C: Find z2 − z1 geometrically and explain your steps.
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Prove that the symmetric matrix is diagonalizable. (Assume that a is real.)
0 0 a
A =
a 0
a 0 0
Find the eigenvalues of A. (Enter your answers as a comma-separated list. Do not list the same eigenvalue multiple times.)
λ=
Find an invertible matrix P such that P-1AP is diagonal.
P =
Which of the following statements is true? (Select all that apply.)
☐ A is diagonalizable because it is a square matrix.
A is diagonalizable because it has a determinant of 0.
A is diagonalizable because it is an anti-diagonal matrix.
A is diagonalizable because it has 3 distinct eigenvalues.
A is diagonalizable because it has a nonzero determinant.
A is diagonalizable because it is a symmetric…
A polar curve is represented by the equation r1 = 7 + 4cos θ.Part A: What type of limaçon is this curve? Justify your answer using the constants in the equation.Part B: Is the curve symmetrical to the polar axis or the line θ = pi/2 Justify your answer algebraically.Part C: What are the two main differences between the graphs of r1 = 7 + 4cos θ and r2 = 4 + 4cos θ?
Elementary Statistics: Picturing the World (7th Edition)
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